1. Field of the Invention
This invention relates to multiple frequency modulation systems and methods, and more particularly to the modulation of an optical beam at two modulation frequencies that are subject to third order intermodulation distortion (IMD).
2. Description of the Related Art
IMD is a major obstacle in the design of an optimum multi-channel optical signal transmission system. It sets a practical limit to the degree of linearity over the dynamic range of the system, and limits the dynamic range itself. The lower end of the system's dynamic range is set by its noise floor, while the upper end is set by the IMD. The upper limit for the input power is the drive level at which the IMD terms begin to exceed the level of the noise floor. The system's distortion-free dynamic range is defined as the difference between the lower and upper drive levels.
IMD results when an optical beam is modulated by a radio frequency (rf) signal having two modulation frequencies .omega..sub.1 and .omega..sub.2. The modulating signal frequencies interact within the beam and produce higher order modes that can lead to distortion. When an electrical modulation signal is used to modulate the beam through an electro-optic coupler, the ratio of output to input optical powers may be expressed as: ##EQU1## where T.sub.0, T.sub.1, T.sub.2, . . . are the gain coefficients for the zero, first, second, . . . order modulation signals, V.sub.0 is a DC offset value, V.sub.1 =A.sub.1 cos.omega..sub.1 t+A.sub.2 cos.omega..sub.2 t, A.sub.1, A.sub.2 are constants.
The first order signal represents a linear gain, in which the input signals are reproduced without distortion. The second order signal is the result of two waves interacting within the beam, the third order signal is the result of three waves mixing, etc. The frequency components of the higher order terms are as follows:
second order: .omega..sub.1 .+-..omega..sub.2, 2.omega..sub.1, 2.omega..sub.2 PA1 third order: 2.omega..sub.1 .+-..omega..sub.2, 2.omega..sub.2 .+-..omega..sub.1, 3.omega..sub.1, 3.omega..sub.2 PA1 fourth order: 4.omega..sub.1, 4.omega..sub.2, 3.omega..sub.1 .+-..omega..sub.2, 3.omega..sub.2 .+-..omega..sub.1, 2.omega..sub.2 .+-.2.omega..sub.1 PA1 fifth order: 5.omega..sub.1, 5.omega..sub.2, 4.omega..sub.1 .+-..omega..sub.2, 4.omega..sub.2 .+-..omega..sub.1, 3.omega..sub.1 .+-.2.omega..sub.2, 3.omega..sub.2 .+-.2.omega..sub.1, 2.omega..sub.2 .+-.3.omega..sub.1, 2.omega..sub.2 .+-..omega..sub.1, 2.omega..sub.1 .+-..omega..sub.2
The gain coefficients for the second and higher order effects are less than unity, and progressively decrease as the order increases. The frequency range can generally be selected so that the second order effects can be filtered from the output, leaving the third order IMD as the limiting factor in dynamic range.